Theory of Multidimensional Solitons

TL;DR

This paper reviews the theory and various phenomena of multidimensional solitons in Bose-Einstein condensates, covering dark and bright solitons, their stability, interactions, and complex structures in higher dimensions.

Contribution

It provides a comprehensive overview of higher-dimensional solitons in Bose-Einstein condensates, highlighting recent theoretical developments and classifications.

Findings

Classification of dark and bright solitons in higher dimensions

Analysis of stability and instability mechanisms

Descriptions of complex soliton structures like vortex rings

Abstract

We review a number of topics germane to higher-dimensional solitons in Bose-Einstein condensates. For dark solitons, we discuss dark band and planar solitons; ring dark solitons and spherical shell solitons; solitary waves in restricted geometries; vortex rings and rarefaction pulses; and multi-component Bose-Einstein condensates. For bright solitons, we discuss instability, stability, and metastability; bright soliton engineering, including pulsed atom lasers; solitons in a thermal bath; soliton-soliton interactions; and bright ring solitons and quantum vortices. A thorough reference list is included.